Method and apparatus for opportunistic user scheduling of two-cell multiple user MIMO

ABSTRACT

An apparatus and a method for opportunistic user scheduling of two-cell multiple user Multiple Input Multiple Output (MIMO) by a base station, the method comprising: broadcasting signals through random beams to users; and receiving Channel Quality Information (CQI) from best K user set. The CQI is calculated based on all possible combinations of transmit beamforming vectors.

PRIORITY

This application claims priority under 35 U.S.C. §119(e) to U.S.Provisional Application No. 61/532,610, which was filed in the U.S.Patent and Trademark Office on Sep. 9, 2011, the entire content of whichis incorporated herein by reference.

1. Field of the Invention

The present invention relates generally to two-cell multiple userMultiple Input Multiple Output (MIMO), and more particularly, to amethod and an apparatus for opportunistic user scheduling of two-cellmultiple user MIMO.

2. Background Art

Over the past few years, a significant amount of research has gone intomaking various techniques for enhancing spectrum reusability reality.The spatial diversity techniques such as MIMO wireless systems have beenwidely studied to improve the spectrum reusability. Recently, the scopeof the spatial diversity is extended to MIMO network wireless systemsincluding the interference network, relay network, and multicellularnetwork. Network MIMO systems are now an emphasis of IMT-Advanced andbeyond systems. In these networks, out-of-cell (or cross cell)interference is a major drawback. Network MIMO systems, when properlydesigned, could allow coordination between nodes that would increase thequality of service in an interference limited area. Before network MIMOcan be deployed and used to its full potential, there are a large numberof challenging issues. Many of these deal with joint processing betweennodes (e.g., see the references in D. Gesbert, S. Hanly, H. Huang, S.Shamai, O. Simeone, and W. Yu, “Multi-cell MIMO cooperative networks: anew look at interference,” IEEE Jour. Select. Areas in Commun., vol. 28,no. 9, pp. 1380-1408, December 2010).

Interference alignment is transmitters/receivers joint processing thatgenerates an overlap of signal spaces occupied by undesired interferenceat each receiver while keeping the desired signal spaces distinct (e.g.,see the references in V. Cadambe and S. Jafar, “Interference alignmentand degrees of freedom of the k-user interference channel,” IEEE Trans.Info.Theory, vol 54, no. 8, pp. 3425-3441, August 2008. and C. Suh andD. Tse, “Interference Alignment for Cellular Networks,” Proc. OfAllerton Conference on Communication, Control, and Computing, September2008. and V. Cadambe and S. Jafar, “Interference alignment and thedegrees of freedom of wirelessX networks,” IEEE Trans. Info.Theory, vol55, no. 9, pp. 3893-3908, September 2009.). However, the jointprocessing between transmitters and receivers for interference alignmentrequires full channel knowledge at all nodes, which is arguablyunrealistic. Recent work on the limited feedback explores the scales ofthe required feedback bits with respect to the required throughput orSINR (e.g., see the references Thukral and H. Bolcskei, “Interferencealignment with limited feedback,” in Proc. IEEE Inrl. Symposium on Info.Theory, June, 2009. and B. Khoshnevis, W. Yu, and R. Adve, “Grassmannianbeamforming for MIMO amplify-and-forward relaying,” IEEE Journals onSel. Areas in Commun., vol. 26, pp. 1397-1407, August 2008.). However,the amount of CSI feedback in (e.g., see the references in Thukral andH. Bolcskei, “Interference alignment with limited feedback,” in Proc.IEEE Inrl. Symposium on Info. Theory, June, 2009. and B. Khoshnevis, W.Yu, and R. Adve, “Grassmannian beamforming for MIMO amplify-and-forwardrelaying,” IEEE Journals on Sel. Areas in Commun., vol. 26, pp.1397-1407, August 2008.) to ensure the required performance is excessiveand only gives marginal performance improvement per additional feedback.In addition, the feedback scheme in (e.g., see the references in Thukraland H. Bolcskei, “Interference alignment with limited feedback,” inProc. IEEE Inrl. Symposium on Info. Theory, June, 2009. and B.Khoshnevis, W. Yu, and R. Adve, “Grassmannian beamforming for MIMOamplify-and-forward relaying,” IEEE Journals on Sel. Areas in Commun.,vol. 26, pp. 1397-1407, August 2008.) assumes huge information sharingbetween backhauls of the transmitter.

SUMMARY OF THE INVENTION

Accordingly, the present invention is designed to address at least theproblems and/or disadvantages described above and to provide at leastthe advantages described below.

Accordingly, an aspect of the present invention is to provide a methodfor opportunistic user scheduling of two-cell multiple user MIMO.

In accordance with an aspect of the present invention, a method isprovided for opportunistic user scheduling of two-cell multiple userMIMO by a base station, the method comprising: broadcasting signalsthrough random beams to users; and receiving Channel Quality Information(CQI) from best K user set. The CQI is calculated based on all possiblecombinations of transmit beamforming vectors.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features, and advantages of certainembodiments of the present invention will be more apparent from thefollowing detailed description when taken in conjunction with theaccompanying drawings, in which:

FIG. 1. illustrates system model choosing the best K user among j userson two-cell multiple user broadcasting channel;

FIG. 2 illustrates system model when the best K users Π={π₁, . . . ,π_(K)} are scheduled in each of cells;

FIG. 3 illustrates sumrates per cell for MIUS schemes;

FIG. 4 illustrates sumrate performance for MSUS schemes; and

FIG. 5 illustrates sumrate performance for MSUS employing 6bits and8bits of matrix codebook.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

Various embodiments of the present invention will now be described indetail with reference to the accompanying drawings. In the followingdescription, specific details such as detailed configuration andcomponents are merely provided to assist the overall understanding ofthese embodiments of the present invention. Therefore, it should beapparent to those skilled in the art that various changes andmodifications of the embodiments described herein can be made withoutdeparting from the scope and spirit of the present invention. Inaddition, descriptions of well-known functions and constructions areomitted for clarity and conciseness.

In this work, we investigate the opportunistic user scheduling ininterfering multiuser MIMO network where J users are associated witheach transmitter and the selected K users together with theirtransmitters construct a two-cell multiuser MIMO broadcast channel.Other than feeding back excessive amount of CSI to transmitter, weconsider a scenario where each transmitter broadcasts random beams(known at both sides of the transmitter and receiver) to users and theuser sends back its CQI to transmitter for the opportunistic userselection. Backhaul between transmitters to allow information sharing isnot assumed. We present exhaustive user scheduling approach andopportunistic user alignment scheme based on the interference alignmentapproach in (e.g., see the references in T. Kim, D. Love, and B.Clerckx, “Spatial Degrees of Freedom of the Multicell MIMO MAC,”submitted in IEEE Global Communications, April, 2011.). For theexhaustive user scheduling, random beams are the actual transmit beams,but in the opportunistic user alignment the random beams are not theactual transmit beams. It is rather used for selecting users and oncethe users are selected transmit beams are designed at the transmitter.For each case, we define efficient CQI measure to be fed back totransmitter for user scheduling and we also address the optimal designof the post processing matrix to minimize the interference (inter userinterference+out-of-cell interference or out-of-cell interference) or tomaximize the sumrate.

1. System Model

FIG. 1. Illustrates system model choosing the best K user among j userson two-cell multiple user broadcasting channel.

Referring to FIG. 1, the base station has M antennas and each user isequipped with N antennas. There are total J users in the cell and only Kusers (K≦J) are selected and served by each BS. We use an index mj todenote the jth user in the cell m, where j∈J and J={1, . . . , J}.

We use an index mπ_(k) to indicate kth scheduled user in cell m wherek∈Π={π₁, . . . , π_(K)}⊂J.

We assume that each user has N=Kβ antennas and each base station isequipped with M=Kβ+β antennas. The base station sends Kβ streams toprovide β streams to each of K users in the cell. The transmitter has noaccess for the perfect channel state information (CSI) at users, ratherit has partial CSI for scheduling users. CSI sharing among base stationsthrough backhaul is not allowed and only partial CSI from serving usersis available at the base station.

In the first step, the base station m broadcasts signals through Krandom beams {V_(mi)}_(i∈K), K={1, . . . , K}, to users whereV_(mi)∈C^((Kβ+β)×β) and V*_(mi)V_(mi)=I_(β). Then, the received signalat jth user in the cell m can be determined as shown in Equation (1).Y _(mj) =H _(mj,m) s _(m) +H _(mj,m) s _(m) +z _(mj)  (1)

In Equation (1), m is defined as m={1,2}\m. The H_(mj,m)∈C^(N×M) denotesthe channel matrix from the base station m to user mj. We assume therealizations of the channels {H_(mj,m)}_(m∈{1,2},j∈j) are mutuallyindependent and each entries of H_(mj,m) has independent and identicalcontinuous distribution. The transmit signal from the base station m canbe determined as shown in Equation (2).s _(m)=Σ_(i=1) ^(K) V _(mi) x _(mi)  (2)

Further, transmit power is constrained tr(E[s_(m)s*_(m)])≦P, which canbe written as

${{tr}\left( {E\left\lbrack {s_{m}s_{m}^{*}} \right\rbrack} \right)} = {{{tr}\left( {\sum\limits_{i = 1}^{K}\;{V_{m\; i}{E\left\lbrack {x_{m\; i}x_{m\; i}^{*}} \right\rbrack}V_{m\; i}^{*}}} \right)} \leq {P.}}$

We assume equal power transmission for each user and to meet the powerconstraint we assume

${E\left\lbrack {x_{m\; i}x_{m\; i}^{*}} \right\rbrack} = {\frac{P}{K\;\beta}.}$

Now, plugging Equation (2) into Equation (1) returns to Equation (3).Y _(mj)=Σ_(i=1) ^(K) H _(mj,m) V _(mi) x _(mi)+Σ_(i=1) ^(K) H _(mj,m) V_(mi) x _(mi) +z _(mj).  (3)

To enable the user scheduling at the base station, each user measureschannel quality information based on its own channel H_(mj,m),out-of-cell interference channel H_(mj,m) , and random beams{V_(mi)}_(i∈K) where the transmitter and receiver share the same randombeam generation method.

FIG. 2 Illustrates system model when the best K users Π={π₁, . . . ,π_(K)} are scheduled in each of cells.

Referring to FIG. 2, for Instance, the scheduled user index is given by{11, . . . , 1k} and {21, . . . , 2k}.

2. Exhaustive User Searching

User mj calculates Channel Quality Information (CQI) for all thepossible combinations of transmit beamforming vectors {V_(mi)}_(i∈K).Prior to define CQIs for exhaustive user scheduling, first severalquantities are defined below.

${SIG}_{{mj},i} = {{E\left\lbrack {\left( {H_{{mj},m}V_{m\; i}x_{m\; i}} \right)\left( {H_{{mj},m}V_{m\; i}x_{m\; i}} \right)^{*}} \right\rbrack} = {\frac{P}{K\;\beta}H_{{mj},m}V_{m\; i}V_{m\; i}^{*}H_{{m\; j},m}^{*}}}$$= {{E\left\lbrack {\left( {\sum\limits_{l \neq i}^{K}\;{H_{{mj},m}V_{ml}x_{m\; l}}} \right)\left( {\sum\limits_{l \neq i}^{K}\;{H_{{mj},m}V_{m\; l}x_{ml}}} \right)^{*}} \right\rbrack} = {\frac{P}{K\;\beta}H_{{mj},m}{\sum\limits_{l \neq k}^{K}\;{V_{m\; l}V_{m\; l}^{*}H_{{mj},m}^{*}}}}}$${= {{E\left\lbrack {\left( {\sum\limits_{i = 1}^{K}\;{H_{{mj},\overset{\_}{m}}V_{\overset{\_}{m}\; l}x_{\overset{\_}{m}\; l}}} \right)\left( {\sum\limits_{l = 1}^{K}\;{H_{{mj},\overset{\_}{m}}V_{\overset{\_}{m}\; l}x_{\overset{\_}{m}\; l}}} \right)^{*}} \right\rbrack} = {\frac{P}{K\;\beta}H_{{mj},\overset{\_}{m}}}}}\;$

SIG_(mj,i) denotes signal covariance matrix at user mj (when V_(mi) isused for the transmission), INT_(IU,mj,K\i) denotes the inter userinterference covariance matrix at user mj (when V_(mi) is used for thetransmission), and INT_(IC,mj) indicates out-of-cell interferencecovariance matrix at user mj. Then, the achievable rate at user mj afterpost processing with a post processing matrix W_(mj,i)∈C^(N×β) (withW*_(mj,i)W_(mj,i)=I_(β)) can be determined as shown in Equation (4).

$\begin{matrix}{R_{{mj},i} = {E\mspace{11mu}{\log_{2}\left( \frac{{I_{\beta} + {{w_{{m\; j},i}^{*}\left( {{SIG}_{{mj},i} + {INT}_{{IU},{mj},{K\backslash i}} + {INT}_{{IC},{mj}}} \right)}W_{{mj},i}}}}{{I_{\beta} + {{w_{{mj},i}^{*}{()}}W_{{mj},i}}}} \right)}}} & (4)\end{matrix}$

In Equation (4), the post processing matrix W_(mj,i) can be determinedby minimizing the interference terms INT_(IU,mj,i)+INT_(IC,mj,i) or bymaximizing the achievable rate. We first elaborate how we canconveniently choose CQI when W_(mj,i) is designed to mitigateINT_(IU,mj,i)+INT_(IC,mj,i). Then, we address the case when W_(mj,i) isdetermined to maximize R_(mj,i).

2.1 Minimum Interference (Inter-user Interference+Out-of-cellInterference) User Scheduling

In this case, the post processing matrix is determined to mitigateINT_(IU,mj,i)+INT_(IC,mj,i). Without loss of generality, we define therate achievable with infinite number of users scheduling (J=∞) asR_(mj,i) ^(∞)=E log₂(|I_(β)+{tilde over (W)}*_(mj,i)SIG_(mπ) _(k) {tildeover (W)}_(mj,i)|).

$\begin{matrix}{{R_{{m\; j},i}^{\infty} - R_{{mj},i}} = {{{{E\;{\log_{2}\left( {{I_{\beta} + {{\overset{\sim}{W}}_{{mj},i}^{*}{SIG}_{m\;\pi_{k}}{\overset{\sim}{W}}_{{mj},i}}}} \right)}} - {E\;{\log_{2}\left( \frac{{I_{\beta} + {{W_{{mj},i}^{*}\left( {{SIG}_{{mj},i} + {INT}_{{IU},{mj},{k\backslash i}} + {{INT}_{{IC},{mj}}}} \right)}W_{{mj},i}}}}{{I_{\beta} + {{W_{{mj},i}^{*}\left( {{INT}_{{IU},{mj},{K\backslash i}} + {INT}_{{IC},{mj}}} \right)}W_{{mj},i}}}} \right)}}} \leq {E\;{\log_{2}\left( {{I_{\beta} + {{W_{{mj},i}^{*}{()}}W_{{mj},i}}}} \right)}}} = {{E\mspace{11mu}{{tr}\left( {\log_{2}\left( {I_{\beta} + {{W_{{mj},i}^{*}{()}}W_{{mj},i}}} \right)} \right)}} \leq {E\mspace{11mu}{{tr}\left( {{W_{{mj},i}^{*}{()}}W_{{mj},i}} \right)}}}}} & (5)\end{matrix}$

From Equation (5), the CQI at user mj when V_(mi) is used for thetransmission can be determined as shown in Equation (6).α_(mj,i)=min_(ŵ) _(mj,i) tr(Ŵ_(mj,i)*(INT_(IU,mj,K\i)+INT_(IC,mj))Ŵ_(mj,i))  (6)

Let the eigenvalue decompositionINT_(IU,mj,K\i)+INT_(IC,mj)=U_(mj)Σ_(mj)U*_(mj). Then, the optimalfilter weight W_(mj,i) that minimizestr(Ŵ_(mj,i)*(INT_(IU,mj,K\i)+INT_(IC,mj))Ŵ_(mj,i)) is determined byW_(mj,i)=[u_(mj,N−β+1) . . . u_(mj,N)] where u_(mj,i) denotes the ithcolumn of U_(mj).

Given CQI defined in Equation (6), user mj feeds back {α_(mj,i)}_(i∈K),i.e., user mj evaluates interference (inter-userinterference+out-of-cell interference) powers corresponding to each of Kbeam forming vectors. Then, receiver m determines the best K user setΠ={π₁, . . . , π_(K)}⊂j to minimize the sum interference as shown inEquation (7).Π={π₁, . . . , π_(K)}=argmin_({tilde over (Π)}={{tilde over (π)}) ₁_(, . . . , {tilde over (π)}) _(K) _(}⊂j) Σ_(i=1)^(K)α_(m{tilde over (π)}) _(i) _(,i)  (7)

In Equation (4), {tilde over (Π)}={{tilde over (π)}₁, . . . , {tildeover (π)}_(K)} with {tilde over (π)}₁≠{tilde over (π)}₂≠ . . . ≠{tildeover (π)}_(K) denotes the all the possible K user permutation in J.Hence, finding the optimal user set Π={π₁, . . . , π_(K)} requires total

${\begin{pmatrix}I \\K\end{pmatrix}K}!=\frac{J!}{\left( {J - K} \right)!}$times of computations of Σ_(i=1) ^(K)α_(m{tilde over (π)}) _(i) .

2.2 Maximum Sumrate User Scheduling

In this case, the post processing matrix is determined to maximizeR_(mj,i) in Equation (4). For simplicity, denoteINT_(mj,i)=INT_(IU,mj,K\i)+INT_(IC,mj).

Then, R_(mj,i) in Equation (4) is lower bounded by Equation (8).

$\begin{matrix}{R_{{mj},i} = {{E\mspace{11mu}{\log_{2}\left( \frac{\left. I_{\beta} \middle| {{W_{{mj},i}^{*}\left( {SIG}_{{mj},i} \middle| {INT}_{{mj},i} \right)}W_{{mj},i}} \right.}{{I_{\beta} + {{W_{{mj},i}^{*}\left( {INT}_{{mj},i} \right)}W_{{mj},i}}}} \right)}} \geq {E\mspace{11mu}{\log_{2}\left( \frac{{{W_{{m\; i},i}^{*}\left( {SIG}_{{mj},i} \right)}W_{{mj},i}}}{{I_{\beta} + {{W_{{mj},i}^{*}\left( {INT}_{{mj},i} \right)}W_{{mj},i}}}} \right)}{\ldots\mspace{14mu}.}}}} & (8)\end{matrix}$

The optimal W_(mj,i) that maximize the lower bound of Equation (8) isfound as follows.

With a congruence transformation, there exists X_(mj)∈C^(N×N) such that:X*hd mjSIG_(mj,i) X _(mj)=diag(c ₁ , . . . , c _(N))=C_(d)  (9)

where c₁≧c₂≧ . . . ≧c_(N)≧0, andX* _(mj)(I _(N)+INT_(mj,i))X _(mj)=diag(s ₁ , . . . , s _(N))=S_(d)  (10)

where s_(N)≧s_(N−1)≧ . . . ≧s₁>0. Then, from Equation (9) and Equation(10), X*_(mj)SIG_(mj,i)X_(mj)C_(d)⁻¹=X*_(mj)(I_(N)+INT_(mj,i))X_(mj)S_(d)⁻¹SIG_(mj,i)X_(mj)=(I_(N)+INT_(mj,i))X_(mj)S_(d) ⁻¹C_(d)

Implying

$\;{{{{SIG}_{{mj},i}x_{{m\; i},1}} = {{\frac{c_{1}}{s_{1}}\left( {I_{N} + {INT}_{{mj},i}} \right)x_{{mj},1}} = {{\lambda_{l}\left( {I_{N} + {INT}_{{mj},i}} \right)}x_{{mj},1}}}},}$where x_(mj,l) denotes the lth column of X_(mj) for l=1,2, . . . , N.Thus,

$\lambda_{l} = \frac{c_{l}}{s_{l}}$is the generalized eigenvalue of SIG_(mj,i) and (I_(N)+INT_(mj,i)) suchthat λ₁≧λ₂≧ . . . ≧λ_(N).

Hence,

$\frac{{{W_{{mj},i}^{*}\left( {SIG}_{{mj},i} \right)}W_{{mj},i}}}{{I_{\beta} + {{W_{{mj},i}^{*}\left( {INT}_{{mj},i} \right)}W_{{mj},i}}}} \leq {\prod\limits_{i = 1}^{\beta}\;{\lambda_{i}.}}$

The equality is achieved by choosing the first β generalizedeigenvectors associated with the generalized eigenvalues λ₁, λ₂, . . . ,λ_(β), as shown in Equation (11).W _(mj,i) =[x _(mj,1) x _(mj,2) . . . x _(mj,β)]  (11)

Now, given W_(mj,i) in Equation (11), CQI is defined as

$\alpha_{{mj},i} = {{\log_{2}\left( \frac{{{W_{{mj},i}^{*}\left( {SIG}_{{mj},i} \right)}W_{{mj},i}}}{\left. I_{\beta} \middle| {{W_{{mj},i}^{*}\left( {INT}_{{mj},i} \right)}W_{{mj},i}} \right.} \right)}.}$

User mj feeds back {α_(mj,i)}_(i∈K) to receiver m and the receiver mdetermines the best K user's index set Π={π₁, . . . , π_(K)} to maximizethe sum rate such that Π={π₁, . . . , π_(K)}=argmax

$\overset{\sim}{\Pi} = {\left\{ {{\overset{\sim}{\pi}}_{1},\ldots\mspace{14mu},{\overset{\sim}{\pi}}_{K}} \right\} \Subset {J{\sum\limits_{i = 1}^{K}\;}}}$where {tilde over (π)}₁≠{tilde over (π)}₂≠ . . . ≠{tilde over (π)}_(K).

3. Opportunistic Interference Alignment

The exhaustive use scheduling in Section 3 requires

$\frac{J!}{\left( {- K} \right)}$times of calculation for finding the best user ordering. In thissection, we develop a low complex user scheduling scheme which is basedon ordering users in the interference alignment planes {P_(m)}_(m∈{1,2})where P_(m)∈C^(M×N) and P*_(m)P_(m)=I_(N). Now, we rewrite Equation (3)as Equation (12).Y _(mj) =H _(mj,m) P _(m) s _(m) +H _(mj,{tilde over (m)}) P_({tilde over (m)}) s _({tilde over (m)}) +z _(mj)  (12)

In Equation (12),

$s_{m} = {\sum\limits_{i = 1}^{K}\;{V_{m\; i}{x_{m\; i}.}}}$

The V_(mi) satisfies V_(mi)∈C^(N×β) and tr(V*_(mi)V_(mi))=β. We have thesame equality power constraints tr(E[s_(m)s*_(m)])=P and

${E\left\lbrack {x_{mi}x_{mi}^{*}} \right\rbrack} = \frac{P}{K\;\beta}$as in Section 3. In this approach, contrary to Section 3, theinterference alignment plains {P_(m)}_(m∈{1,2}) are not used for datatransmission, but used for scheduling users. Once the users have beenopportunistically scheduled, the transmitter performs zero-forcing bydesigning {V_(mi)}_(i∈K).

The CQI consists of one α_(mj) and one F_(mj)∈C^(β×N). Analogous toSection 3, for scheduling the users, the post processing matrixW_(mj)∈C^(N×β) (with W*_(mj)W_(mj,)=I_(β)) can be determined by minimizethe out-of-cell interference or to maximize the achievable rate.

Define:

SIG_(mj)=E[(H_(mj,m)P_(m)s_(m))(H_(mj,m)P_(m)s_(m))*]=PH_(mj,m)P_(m)P*_(m)H*_(mj,m) and

INT_(IC,mj)=E[(H_(mj,m) P _(m) s _(m) )(H_(mj,m) P _(m) s _(m) )*]=PH_(mj,m) P _(m) P* _(m) H*_(mj,m) ,

where SIG_(mj) denotes the signal covariance matrix at user mj andINT_(IC,mj) denotes the out-of-cell interference covariance matrix atuser mj. Then, the mutual information after post processing betweens_(m) and W*_(mj)Y_(mj) can be expressed as shown in Equation (13)

$\begin{matrix}{I_{mj} = {{\log_{2}\begin{pmatrix}{{I_{\beta} + {{W_{mj}^{*}\left( {{SIG}_{mj} + {INT}_{{IC},{mj}}} \right)}W_{mj}}}} \\{{I_{\beta} + {{W_{mj}^{*}\left( {INT}_{{IC},{mj}} \right)}W_{m\; j}}}}\end{pmatrix}}\mspace{11mu}{\ldots\mspace{14mu}.}}} & (13)\end{matrix}$

3.1 Minimum Out-of-cell Interference User Scheduling

Define CQI at user mj as shown in Equation (14).α_(mj)=min_(Ŵ) _(mj) tr(Ŵ _(mj)*(INT_(IC,mj))Ŵ _(mj))  (14)

Let the eigenvalue decomposition INT_(IC,mj)=U_(mj)Σ_(mj)U*_(mj). Then,the optimal filter weights W_(mj) that minimizestr(Ŵ_(mj)*(INT_(IC,mj))Ŵ_(mj)) is determined by W_(mj)=[u_(mj,N−β+1) . .. u_(mj,N)] where u_(mj,i) denotes the ith column of U_(mj).

Given CQI defined in Equation (4), user mj feeds back one α_(mj) and amatrix F_(mj)∈C^(β×N). The F_(mj) is defined as the direction of thepost processed channel matrix W*_(mj)H_(mj,m)P_(m) where the directionof W*_(mj)H_(mj,m)P_(m) can be extracted by SVDW*_(mj)H_(mj,m)P_(m)=U_(mj)R_(mj)V*_(mj) as F_(mj)=[v_(mj,1) . . .v_(mj,β)]*. Note that we can employ matrix codebook or elementwisequantization for delivering F_(mj) to the base station m.

Then, receiver m determines K user set Π={π₁, . . . , π_(K)} to minimizethe sum out-of-cell interference such that

${\Pi = {\left\{ {\pi_{1},\ldots\mspace{14mu},\pi_{K}} \right\} = {{\arg\;\min_{\overset{\sim}{\Pi} = {\{{{\overset{\sim}{\pi}}_{1},\mspace{11mu}\ldots\mspace{14mu},{\overset{\sim}{\pi}}_{K}}\}}}} \Subset {J{\sum\limits_{i = 1}^{K}\;}}}}},$where {tilde over (Π)}={{tilde over (π)}₁, . . . , {tilde over (π)}_(K)}with {tilde over (π)}₁≠{tilde over (π)}₂≠ . . . ≠{tilde over (π)}_(K)denotes the all possible K user combinations in J. Hence, finding theoptimal user set Π={π₁, . . . , π_(K)} requires total

$\begin{pmatrix}J \\K\end{pmatrix} = \frac{J!}{{K!}{\left( {J - K} \right)!}}$times of computation for Σ_(i=1) ^(K)α_(m{tilde over (π)}) _(i) _(,i).The complexity for finding Π={π₁, . . . , π_(K)} can be decreased if weuse an efficient sorting algorithms for sorting all {α_(mj)}_(j∈j) suchthat {α_(mπ) ₁ , . . . , α_(mπ) _(K) }≦{α_(mj)}_(j∈j\Π).

This easily accomplished by using fast sorting algorithms which usuallyrequires on average J log₂(J) comparisons. If we consider one additionis equivalent to one comparison, for choosing the user the exhaustivesearch in Section 3 requires total

$\frac{J!}{\left( {- K} \right)!}K$times of additions while the opportunistic interference alignmentrequires only J log₂(J) times of comparisons.

After selecting the users Π={π₁, . . . , π_(K)} the transmitterdetermines the transmit filter weight as zero-forcing weight. Consider astacked matrix

$F_{m\;\Pi} = \begin{bmatrix}F_{m\;\pi_{1}} \\F_{m\;\pi_{2}} \\\vdots \\F_{m\;\pi_{K}}\end{bmatrix}$

and the inverse of F_(mΠ) as F_(mΠ) ⁻¹={tilde over (V)}_(mΠ). To meetthe power constraint each column of {tilde over (V)}_(mΠ) is normalizedas one and we denote the normalized one as V_(mΠ). Then, thezero-forcing transmit vectors {V_(mπ) _(i) }_(i∈Π) for users{mπ_(i)}_(i∈Π) are mapped by V_(mΠ)=[V_(mπ) ₁ V_(mπ) ₂ . . . V_(mπ) _(K)].

3.2 Maximizing Sumrate User Scheduling

The I_(mj) in Equation (13) is lower bounded as shown in Equation (15).

$\begin{matrix}{I_{mj} = {{\log_{2}\begin{pmatrix}{{I_{\beta} + {{w_{mj}^{*}\left( {{SIG}_{mj} + {INT}_{{IC},{mj}}} \right)}w_{mj}}}} \\{{I_{\beta} + {{w_{mj}^{*}\left( {INT}_{{IC},{mj}} \right)}w_{mj}}}}\end{pmatrix}} \geq {E\mspace{11mu}{\log_{2}\left( \frac{{{W_{mj}^{*}\left( {SIG}_{mj} \right)}W_{mj}}}{{I_{\beta} + {{W_{mj}^{*}\left( {INT}_{{IC},{m\; i}} \right)}W_{mj}}}} \right)}{\ldots\mspace{14mu}.}}}} & (15)\end{matrix}$

The optimal W_(mj) that maximize the lower bound of Equation (15) is thefirst β generalized eigenvectors of (SIG_(mj), I_(N)+INT_(IC,mj)).Analogous with Section 3.2, we define the generalized eigenvalue matrixof (SIG_(mj), I_(N)+INT_(IC,mj)) as X_(mj) where the ith columns ofX_(mj) corresponds to ith dominant eigenvalue λ_(i). Hence, the bound ofEquation (15) is maximized by selecting W_(mj) as below shown inEquation (16).W _(mj) =[x _(mj,1) x _(mj,2) . . . x _(mj,β)]  (16)

Now, given W_(mj) in Equation (11), we define the CQI as

$\alpha_{mj} = {{\log_{2}\left( \frac{{{W_{mj}^{*}\left( {SIG}_{mj} \right)}W_{mj}}}{\left. I_{\beta} \middle| {{W_{mj}^{*}\left( {INT}_{{IC},{m\; i}} \right)}W_{m\; j}} \right.} \right)}.}$

User mj feeds back one α_(mj) and a matrix F_(mj)∈C^(β×N) to receiver mand the receiver m determines the best K user's index set Π={π₁, . . . ,π_(K)} to maximize the sum rate such that

${\Pi = {\left\{ {\pi_{1},\ldots\mspace{14mu},\pi_{K}} \right\} = {{\arg\;\max_{\overset{\sim}{\Pi} = {\{{{\overset{\sim}{\pi}}_{1},\ldots\mspace{14mu},{\overset{\sim}{\pi}}_{K}}\}}}} \Subset {J{\sum\limits_{i = 1}^{K}\;{\alpha_{m{\overset{\sim}{\pi}}_{i}}}}}}}},$where {tilde over (π)}₁≠{tilde over (π)}₂≠ . . . ≠{tilde over (π)}_(K).

After selecting the users Π={π₁, . . . , π_(K)} the transmitterdetermines the transmit filter weight as zero-forcing weight. Consider astacked matrix:

${F_{m\;\Pi} = \begin{bmatrix}F_{m\;\pi_{1}} \\F_{m\;\pi_{2}} \\\vdots \\F_{m\;\pi_{K}}\end{bmatrix}},$and the inverse of F_(mΠ) as F_(mΠ) ⁻¹={tilde over (V)}_(mΠ). To meetthe power constraint each column of {tilde over (V)}_(mΠ) is normalizedas one and we denote the normalized one as V_(mΠ). Then, thezero-forcing transmit vectors {V_(mπ) _(i) }_(i∈Π) for users{mπ_(i)}_(i∈Π) are mapped by V_(mΠ)=[V_(mπ) ₁ V_(mπ) ₂ . . . V_(mπ) _(K)].

In this section, we evaluate the proposed user scheduling schemes wherethe transmitter serves the best K=2 users among J users. The numbers ofthe transmit antennas and receive antennas are given by M=Kβ+β and N=Kβ.Throughout the simulation we assume single date stream transmission peruser, we use MIUS to denote the minimum interference user scheduling(MIUS) presented in Section 2.1 and 3.1, and MSUS is used to denote themaximum sumrate user scheduling (MSUS) in Section 2.2 and 3.2.

FIG. 3 Illustrates sumrates per cell for MIUS schemes.

Referring to FIG. 3, ‘Exhaustive’ implies exhaustive user schedulingscheduling scheme in Section 2 and ‘OIA’ denotes the opportunisticinterference alignment scheme in Section 3. Exhaustive user searchingonly needs to feedback K real CQI values {α_(mj,i)}_(i∈K) and OIArequires to send back one real CQI α_(mj) and the direction of the postprocessed channel matrix F_(mj)∈C^(1×K) which is composed of 2K realvalues. The exhaustive user scheduler at the receiver need to compute

$\frac{J!}{\left( {- K} \right)!}K$folds of computation, while the OIA only needs to compute J log₂(J)folds of operations. As can be seen from FIG. 3, OIA shows betterperformance. As SNR increases the throughput enhancement for OIA issignificant compared to exhaustive user selection.

FIG. 4 Illustrates sumrate performance for MSUS schemes.

Referring to FIG. 4, Compared to MIUS, MSUS yields higher throughputgain because the post processing matrix is chosen to maximize theindividual throughput. The similar trend is observed as FIG. 3. However,compared to FIG. 3, the optimality of the post processing matrix designin MSUS promises the significant throughput gain especially for OIA.

In FIG. 3 and FIG. 4, we consider the feedback scenario where each userin OIA feeds back 2K+1 real scalars. In this simulation study, weinvestigate the effect of the quantization error when we employ thematrix codebook to quantize the post processed channel F_(mj)∈C^(1×K).

FIG. 5 illustrates the sumrate performance for MSUS when we employ 6bitsand 8bits of matrix codebook. For the sake of the simplicity thecodebook is randomly generated.

As can be seen from the FIG. 5, OIA can achieve better performance thanexhaustive user searching at high SNR with reduced feedback amount.

While the present invention has been particularly shown and describedwith reference to certain embodiments thereof, it will be understood bythose of ordinary skill in the art that various changes in form anddetails may be made therein without departing from the spirit and scopeof the present invention as defined by the following claims and theirequivalents.

What is claimed is:
 1. A method for opportunistic user scheduling of amulti-user multiple input multiple output (MIMO) by a base station, themethod comprising: broadcasting signals through a set of randomlygenerated beamforming vectors; receiving channel quality information(CQI) from each of user terminals that receive the broadcasted signals;and determining a best user set among the user terminals based on theCQI and inter-user interference of the user terminals, wherein a numberof beamforming vectors included in the set of randomly generatedbeamforming vectors is equal to a number of user terminals included inthe best user set, wherein the CQI comprises CQI values corresponding tothe beamforming vectors, respectively, wherein each of the CQI valuescorresponding to the beamforming vectors is determined based on a postprocessing matrix to be applied to the broadcasted signals, and aninter-user interference and an out-of-cell interference when acorresponding beamforming vector is used for transmission, wherein thepost processing matrix for the corresponding beamforming vector isdetermined to maximize an achievable rate after post processing with thepost processing matrix to be applied to the broadcasted signals when thecorresponding beamforming vector is used for transmission, and whereinthe achievable rate after post processing is calculated based on asignal when the corresponding beamforming vector is used fortransmission, the inter-user interference and the out-of-cellinterference when the corresponding beamforming vector is used fortransmission.
 2. The method of claim 1, wherein the best user set isdetermined to minimize sum interference in each of at least two cells.3. The method of claim 2, wherein the sum interference is calculated byadding the inter-user interference to out-of-cell interference.
 4. Themethod of claim 1, wherein the best user set is determined to maximizesum rate in each of at least two cells.
 5. The method of claim 1,wherein the best user set is determined to minimize sum out-of-cellinterference in each of at least two cells.
 6. A method foropportunistic user scheduling of a multi-user multiple input multipleoutput (MIMO) by a user terminal, the method comprising: receiving asignal broadcasted from a base station through a set of randomlygenerated beamforming vectors; determining channel quality information(CQI) based on the received signal; and transmitting the CQI to the basestation, wherein a best user set is determined based on CQI of each ofuser terminals including the user terminal and the other user terminalsand inter-user interference of the user terminals, and wherein the CQIcomprises CQI value corresponding to the beamforming vectors,respectively wherein a number of beamforming vectors included in the setof randomly generated beamforming vectors is equal to a number of userterminals included in the best user set, wherein the CQI comprises CQIvalues corresponding to the beamforming vectors respectively, whereineach of the CQI values corresponding to the beamforming vectors isdetermined based on a post processing matrix to be applied to thebroadcasted signals, and an inter-user interference and an out-of-cellinterference when a corresponding beamforming vector is used fortransmission. wherein the post processing matrix for the correspondingbeamforming vector is determined to maximize an achievable rate afterpost processing with the post processing matrix to be applied to thebroadcasted signals when the corresponding beamforming vector is usedfor transmission, and wherein the achievable rate after post processingis calculated based on a signal when the corresponding beamformingvector is used for transmission, the inter-user interference and theout-of-cell interference when the corresponding beamforming vector isused for transmission.
 7. The method of claim 6, wherein the best userset is determined to minimize sum interference in each of at least twocells.
 8. The method of claim 7, wherein the sum interference iscalculated by adding the inter-user interference to out-of-cellinterference.
 9. The method of claim 6, wherein the best user set isdetermined to maximize sum rate in each of at least two cells.
 10. Themethod of claim 6, wherein the best user set is determined to minimizesum out-of-cell interference in each of at least two cells.
 11. Anapparatus for opportunistic user scheduling of multi-user multiple inputmultiple output (MIMO), the apparatus comprising: a communication moduleconfigured to broadcast signals through a set of randomly generatedbeamforming vectors, and to receive channel quality information (CQI)from each of user terminals that receive the broadcasted signals, and acontroller configured to determine a best user set among the userterminals based on the CQI and inter-user interference of the userterminals, wherein a number of beamforming vectors included in the setof randomly generated beamforming vectors is equal to a number of userterminals included in the best user set, wherein the CQI comprises CQIvalues corresponding to the beamforming vectors, respectively, whereineach of the CQI values corresponding to the beamforming vectors isdetermined based on a post processing matrix to be applied to thebroadcasted signals, and an inter-user interference and an out-of-cellinterference when a corresponding beamforming vector is used fortransmission, wherein the post processing matrix for the correspondingbeamforming vector is determined to maximize an achievable rate afterpost processing with the post processing matrix to be applied to thebroadcasted signals when the corresponding beamforming vector is usedfor transmission, and wherein the achievable rate after post processingis calculated based on a signal when the corresponding beamformingvector is used for transmission, the inter-user interference and theout-of-cell interference when the corresponding beamforming vector isused for transmission.
 12. The apparatus of claim 11, wherein the bestuser set is determined to minimize sum interference in each of at leasttwo cells.
 13. The apparatus of claim 12, wherein the sum interferenceis calculated by adding the inter-user interference to out-of-cellinterference.
 14. The apparatus of claim 11, wherein the best user setis determined to maximize sum rate in each of at least two cells. 15.The apparatus of claim 11, wherein the best user set is determined tominimize sum out-of-cell interference in each of at least two cells. 16.A user terminal for opportunistic user scheduling of multi-user multipleinput multiple output (MIMO), the user terminal comprising: acommunication module configured to receive a signal broadcasted from abase station through a set of randomly generated beamforming vectors,and to transmit channel quality information (CQI) to the base station;and a controller configured to determine the CQI based on the receivedsignal, wherein a best user set is determined based on CQI of each ofuser terminals including the user terminal and the other user terminalsand inter-user interference of the user terminals, wherein a number ofbeamforming vectors included in the set of randomly generatedbeamforming vectors is equal to a number of user terminals included inthe best user set, wherein the CQI comprises CQI values corresponding tothe beamforming vectors, respectively, wherein each of the CQI valuescorresponding to the beamforming vectors is determined based on a postprocessing matrix to be applied to the broadcasted signals, and aninter-user interference and an out-of-cell interference when acorresponding beamforming vector is used for transmission, wherein thepost processing matrix for the corresponding beamforming vector isdetermined to maximize an achievable rate after post processing with thepost processing matrix to be applied to the broadcasted signals when thecorresponding beamforming vector is used for transmission, and whereinthe achievable rate after post processing is calculated based on asignal when the corresponding beamforming vector is used fortransmission, the inter-user interference and the out-of-cellinterference when the corresponding beamforming vector is used fortransmission.
 17. The user terminal of claim 16, wherein the best userset is determined to minimize sum interference in each of at least twocells.
 18. The user terminal of claim 17, wherein the sum interferenceis calculated by adding the inter-user interference to out-of-cellinterference.
 19. The user terminal of claim 16, wherein the best userset is determined to maximize sum rate in each of at least two cells.20. The user terminal of claim 16, wherein the best user set isdetermined to minimize sum out-of-cell interference in each of at leasttwo cells.